Optimal scheduling for sequentially connected cluster tools with dual-armed robots and a single input and output module

We examine a cyclic scheduling problem of sequentially connected cluster tools with a single input and output module, which includes multi-cluster tools and linear cluster tools. Every component tool has a dual-armed robot, and chambers are parallelised for a long process step. An intermediate buffer between each pair of adjacent component tools has a limited capacity, and all processed wafers should return to the input and output module. To examine the scheduling problem, we first compute workloads of the process steps and robots to obtain a lower bound on the tool cycle time. We then identify a rule of assigning the chambers to the process steps that makes the tool cycle time independent of the order of using the parallel chambers. We also propose a simple robot task sequence which is modified from the well-known swap sequence for each component tool. We prove that the modified swap sequence is optimal when one of the process steps, not a robot, is the bottleneck. We also present a scheduling strategy which controls robot task timings to deal with interference of wafer flows between each pair of adjacent component tools. Finally, we perform numerical experiments to show the performance of the proposed sequence.